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Purpose This study aims to numerically simulate the flow induced by a radially expanding/contracting and rotating sphere with suction. In the absence of rotation, one-dimensional flow motion occurs as expected. Otherwise, centrifugal force slows down the induced flow motion, in addition to the radial movement of the surface. Design/methodology/approach The present work is devoted to the analysis of a rotating permeable sphere. The sphere, because it is elastic, is allowed to expand or contract uniformly in the radial direction while rotating. Findings Numerical simulations of the governing equation in spherical coordinates are supported by a perturbation approach. It is found that the equatorial region is effectively smoothen out by the wall suction in non-expanding, expanding and contracting wall deformation cases. The radial inward flow in the vicinity of the equator is no longer valid in the case of sphere expansion, and strong suction causes nearly constant radial suction velocities. More fluid is sucked radially inward near the pole region when wall contraction is active. Originality/value The problem is set up for the first time in the literature. It is determined physically, the wall expansion mechanism requires more torque with less drag.

Researchers and academics are interested in nanofluids because of their high heat transmission rates. The researchers develop advanced and cheap procedures for the enhancement of thermal devices and exchangers. Nanofluids are one of the advanced technology approaches to improving the thermal performance of devices. The combination of two nanoparticles of different chemical properties in a single base fluid termed a hybrid nanofluid has the advanced properties to increase heat transfer and destroy bad bacteria. For this purpose, the couple stress Casson hybrid nanofluid is examined in a time-dependent MHD quadratic heat transfer movement in a stagnation region of a revolving sphere with chemical reaction. The flow is produced by a natural rotation of the sphere, which comprises copper oxide, copper nanoparticles in hybrid nanofluid and nanofluid and blood as a common liquid. The OHAM in Mathematica is used to compute this convectional amplitude, and the shooting numerical method has been used to validate the results. The influence of the included modeling components on fluid flow, Nusselt number, energy, concentration, and the skin friction coefficient are assessed numerically and graphically. The results represent that raising values of ϕ 1 , ϕ 2 from 0.01 to 0.02 improves the rate of heat transfer by 5.8% and 11.947%. When hybrid nanomaterial, nanomaterial, and base fluid were compared, it was discovered that hybrid nanomaterial seems to have the most efficient behavior. A comparison of the current investigation with published work is included to support the projected model.

In the present analysis, an unsteady MHD mixed convection flow is scrutinized for a non-Newtonian Casson hybrid nanofluid in the stagnation zone of a rotating sphere, resulting from the impulsive motion of the angular velocity of the sphere and the velocity of the free stream. A set of linearized equations is derived from the governing ones, and these differential equations are solved numerically using the hybrid linearization–differential quadrature method. The surface shear stresses in the x- and y-directions and the surface heat transfer rate are improved due to the Casson βo, mixed convection α, rotation γ and magnetic field M parameters. In addition, as nanoparticles, the solid volume fraction (parameter ϕ) increases, and the surface shear stresses and the rate of heat transfer are raised. A comparison between earlier published data and the present numerical computations is presented for the limiting cases, which are noted to be in very good agreement.

PurposeUnderstanding the mechanical and thermal behavior of materials is the goal of the branch of study known as fractional thermoelasticity, which blends fractional calculus with thermoelasticity. It accounts for the fact that heat transfer and deformation are non-local processes that depend on long-term memory. The sphere is free of external stresses and rotates around one of its radial axes at a constant rate. The coupled system equations are solved using the Laplace transform. The outcomes showed that the viscoelastic deformation and thermal stresses increased with the value of the fractional order coefficients.Design/methodology/approachThe results obtained are considered good because they indicate that the approach or model under examination shows robust performance and produces accurate or reliable results that are consistent with the corresponding literature.FindingsThis study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.Originality/valueThis study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.

This study systematically investigates the evolution of the flow field and cavitation behavior during the underwater launch of a rotating sphere. By comparing surface pressure distribution, cavitation evolution, flow separation locations, and re-entrant jet formation under various rotational conditions, this study reveals the significant influence of rotation on both the cavitation processes and sphere’s motion trajectory. It is found that under rotational conditions, cavity detachment tends to occur earlier on the front side, and the re-entrant jet develops more fully, reaching maximum length and intensity at a moderate angular velocity. In additionally, rotation alters the cavity interface and overall flow structure, resulting in noticeable differences in surface wetting, pressure distribution, and separation behavior between the front and rear sides. As the rotational speed increases, flow separation points become less distinct, and pressure fluctuations on the rear side intensify, indicating that rotation plays a critical role in modulating underwater cavitation dynamics. The findings provide theoretical insights into flow control and cavitation risk assessment for underwater launches of rotating bodies.

Purpose This study aims to examine the flow of unsteady mixed convective hybrid nanofluid over a rotating sphere with heat generation/absorption. The hybrid nanofluid contains different shapes of nanoparticles (copper [Cu] and aluminium oxide [Al2O3]) in the base fluid (water [H2O]). The influence of different shapes (sphere, brick, cylinder, platelets and blades) of nanoparticle in water-based hybrid nanofluid is also investigated. Design/methodology/approach To analyse the nanomaterial, the flow model is established, and in doing so, the Prandtl’s boundary layer theory is incorporated into the present model. The bvp4c approach, i.e. finite difference method, is used to find the numerical solution of differential equations that is controlling the fluid flow. The effect of relevant flow parameters on nanofluid temperature and velocity profile is demonstrated in detailed explanations using graphs and bar charts, whereas numerical results for Nusselt number and the skin’s coefficient for various form parameters are presented in tabular form. Findings The rate of heat transfer is least for spherical-shaped nanoparticle because of its smoothness, symmetricity and isotropic behaviour. The rate of heat transfer is highest for blade-shaped nanoparticles as compared to other shapes (brick, cylindrical and platelet) of nanoparticles because the blade-shaped nanoparticles causes comparatively more turbulence flow in the nanofluid than other shapes of nanoparticle. Heat generation affects the temperature distribution and, hence, the particle deposition rate. The absorption of heat extracts heat and reduce the temperature across the rotating sphere. The heat generation/absorption parameter plays an important role in establishing and maintaining the temperature around the rotating sphere. Research limitations/implications The numerical study is valid with the exception of the fluctuation in density that results in the buoyancy force and the functional axisymmetric nanofluid transport has constant thermophysical characteristics. In addition, this investigation is also constrained by the assumptions that there is no viscosity dissipation, no surface slippage and no chemically activated species. The hybrid nanofluid Al2O3–Cu/H2O is an incompressible and diluted suspension. The single-phase hybrid nanofluid model is considered in which the relative velocity of water (H2O) and hybrid nanoparticles (Al2O3–Cu) is the same and they are in a state of thermal equilibrium. Practical implications Study on convective flow across a revolving sphere has its applications found in electrolysis management, polymer deposition, medication transfer, cooling of spinning machinery segments, spin-stabilized missiles and other industrial and technical applications. Originality/value The originality of the study is to investigate the effect of shape factor on the flow of electrically conducting hybrid nanofluid past a rotating sphere with heat generation/absorption and magnetic field. The results are validated and provide extremely positive balance with the recognised articles. The results of the study provide many appealing applications that merit further study of the problem.

This study examines magnetohydrodynamic (MHD) heat and mass transfer of a ternary hybrid nanofluid over a rotating sphere incorporating thermophoretic particle deposition, thermal radiation, activation energy and chemical reaction effects. The nanofluid consists of – – nanoparticles dispersed in propylene glycol. The governing boundary layer equations are transformed into a system of nonlinear ordinary differential equations via similarity transformations, which are solved using the Gegenbauer wavelet method. Results indicate that increasing magnetic interaction suppresses velocity due to Lorentz force effects while enhancing thermal distribution. Higher nanoparticle volume fraction improves heat transfer but increases viscous resistance. Thermophoresis and activation energy significantly influence mass transfer characteristics. Comparative analysis reveals that the ternary hybrid nanofluid exhibits enhanced thermal performance relative to the corresponding hybrid nanofluid configuration. The findings provide theoretical insight into MHD-controlled rotating nanofluid systems.

To cool a heated rotating sphere, a heat sink with spherical surface is designed which is situated at a small distance from the sphere; thus, a small curve surface air gap is formed between them which will be used to transfer the heat from the rotating sphere. The numerical simulation method was used to investigate the flow and heat transfer capability of the small air gap. In the entire flow region, a regular Eulerian grid was adopted to solve the modified momentum and energy equations simultaneously. In the region that was occupied by the rotating sphere, a moving Lagrangian grid was used, which tracks the rotational motion of the sphere. A Reynolds function and an energy function were introduced to represent the momentum interaction and thermal interaction between the sphere and the fluid. The heat transfer rate and the flow characteristics of the air gap were presented. The influence of rotating speed and eccentricity as well as the radius of curvature on the flow were quantitatively investigated. It was found that the heat transfer strengths could be adjusted by changing these parameters. It was also observed that the eccentricity and the rotating speed exert significant influences on the heat transfer.

The flow of a non-Newtonian, power-law fluid, directed normally to a rotating sphere is considered in the present paper. The problem is investigated by means of a three-dimensional numerical simulation with the SIMPLE algorithm. The investigation covers the power-law index from 0.2 up to 2, rotation rate from 0.1 up to 3 and Reynolds number from 0.1 up to 100. The following general rules are valid. The lift coefficient increases with increasing the rotation rate. At high Re numbers the drag coefficient increases with the power-law index. At high Re numbers the torque coefficient increases with the power-law index and with the rotation rate, whereas the torque coefficient reduces as the Reynolds number increases. In addition, there are some special cases which are analyzed in the text.

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.